What is the integral of (x^6)/((4-x^7)^2) ?

The integral of (x^6)/((4-x^7)^2) is 1/(7(4-x^7))+C

Popular >

integral of (x^6)/((4-x^7)^2)

\int \frac{x ^{6}}{( 4 - x ^{7} ) ^{2}} d x

\frac{1}{7 ( 4 - x ^{7} )} + C

Solution steps

\int \frac{x ^{6}}{( 4 - x ^{7} ) ^{2}} d x

Apply u-substitution

: \int - \frac{1}{7 u ^{2}} d u

= \int - \frac{1}{7 u ^{2}} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{1}{7} \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{7} (- \frac{1}{u})

Substitute back

u = 4 - x^{7}

= - \frac{1}{7} (- \frac{1}{4 - x ^{7}})

Simplify

- \frac{1}{7} (- \frac{1}{4 - x ^{7}}) : \frac{1}{7 ( 4 - x ^{7} )}

= \frac{1}{7 ( 4 - x ^{7} )}

Add a constant to the solution

= \frac{1}{7 ( 4 - x ^{7} )} + C

\frac{d}{d x} (7 sec (x) tan (x))

\int_{2}^{4} e^{3 x - y} d y

\frac{d}{d x} ((3^{\frac{2}{3}} - x^{\frac{2}{3}})^{\frac{3}{2}})

x \to 0 lim (\frac{5 x ^{2}}{2})

y^{^{'}} + \frac{1}{t} y = \frac{1}{t ^{2}}

What is the integral of (x^6)/((4-x^7)^2) ?
The integral of (x^6)/((4-x^7)^2) is 1/(7(4-x^7))+C